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Estimating discriminatory power and PD curves when the number of defaults is small


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  • Dirk Tasche


The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory power. In the second phase of the approach, the raw PD curve is calibrated to fit a target unconditional PD. The concepts and techniques presented include a discussion of different definitions of area under the curve (AUC) and accuracy ratio (AR), a simulation study on the performance of confidence interval estimators for AUC, a discussion of the one-parametric approach to the estimation of PD curves by van der Burgt (2008) and alternative approaches, as well as a simulation study on the performance of the presented PD curve estimators. The topics are treated in depth in order to provide the full rationale behind them and to produce results that can be implemented immediately.

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Paper provided by in its series Papers with number 0905.3928.

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Date of creation: May 2009
Date of revision: Mar 2010
Handle: RePEc:arx:papers:0905.3928

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Cited by:
  1. Dirk Tasche, 2011. "Bayesian estimation of probabilities of default for low default portfolios," Papers 1112.5550,, revised Aug 2013.
  2. Dirk Tasche, 2012. "Bounds for rating override rates," Papers 1203.2287,, revised Aug 2012.


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